Column emptying

As for all partial differential equations, it is also necessary to complement the mass balance equation with initial and boundary conditions, as explained in detail by Guiochon et al. [13]. The initial condition describes the state of the column when the experiment begins, i.e., at t = 0. In this case, the initial condition corresponds to a column empty of sample and containing only mobile and stationary phases in equilibrium ... 

As always with differential equations, the solution of Eq. 6.24 depends on the choice of the initial and boundary conditions. The initial condition in linear chromatography is almost always a column empty of sample, with the two phases in equilibrimn. The problem of the selection of appropriate boimdary conditions for the solution of a partial differential equation is mathematically subtle and full of pitfalls. Boimdary conditions which, for a chromatographer, seem to describe nearly identical experiments may result in different solutions e.g., the next three sub-sections). We give here an example of the problems foimd and show how their solution is important for a proper understanding of the chromatographic process. 

In most cases, chromatography is performed with a simple initial condition, C(f = 0,z) = q t = 0,z) = 0. TTie column is empty of solute and the stationary and mobile phases are under equilibrium. There are some cases, however, in which pulses of solute are injected on top of a concentration plateau (see Chapter 3, Section 3.5.4). The behavior of positive concentration pulses injected xmder such conditions is similar to that of the same pulses injected in a column empty of solute and they exhibit similar profiles. Even imder nonlinear conditions (high plateau concentration), a pulse that is sufficiently small can exhibit a quasi-linear behavior and give a Gaussian elution profile. Its retention time is linearly related to the slope of the isotherm at the plateau concentration. Measuring this slope is the purpose of the pulse method of measurement of isotherm data. Large pulses may also be injected and they will give overloaded elution profiles similar to those obtained with a column empty of solute. 

Profiles in Column IV The initial condition for column IV is a column empty of feed components. The boundary condition is a stream of desorbent containing no component 1 during the initial part of the period. Then, a concentration plateau at Cf appears, followed by a second shock and a plateau at. This second plateau migrates over a distance equal to Lg at time 2t because concentration velocities are independent of the concentrations with a linear, noncompetitive isotherm. The first shock, at Cf migrates an extra distance L (Figure 17.4b). 

The weighted least-squares routine shown below provides the adjustable parameters and their standard deviations. If that is all you need, you may want to use it also as your general least-squares routine, especially after you have incorporated it in a menu or given it a toolbar icon (in which case it is easier to use and more readily accessible than the Regression routine in the Analysis ToolPak). When using it for unweighted least squares, merely leave the second column empty. Alternatively, if you desire the routine to provide more statistical information, you can modify it to do so. Remember, you are at the controls here. 

The apparatus for simple or countercurrent distillation at reduced pressures differs from that used at atmospheric pressure only by its wider dimensions (c/. section 4.11). A few additional components are necessary, such as a vacuum connection, which is generally provided with a cold trap (Fig. 188). Besides packed columns, empty columns (chap. 7.3.1) and columns with stationary (chap. 7.3.4) and rotating... 

U = velocity, ft/sec based on tower superficial area Ug = superficial velocity based on cross-section area of empty column, ft/sec... 

File) (New) A new data file can be generated by defining the number of columns and rows and then filling the table either in a column-by-col-umn or a row-by-row sequence if the option (Leave Empty) is chosen, the file is stored as is. The array size is limited to m < 10, but also by the available memory. 

EDIT.dat A 6-row-by-25-column table containing integer numbers in random and not-so-random sequences a few empty cells are included. Use this file to play with the editing functions contained in program DATA. 

Figure 5.4-7. Empty bubble column. Figure 5.4-8. Packed-bed column reactors.

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